Paolo Gambino Beauty 2005 Assisi 1 Semileptonic and radiative B decays Paolo Gambino INFN Torino.

Paolo Gambino Beauty 2005 Assisi 1

Semileptonic and Semileptonic and radiativeradiativeB decaysB decays

Paolo Gambino INFN Torino


A set of interdependent measurements

b→c l ν treeBR~10

%|Vcb|

b→u l ν tree ~10-3 |Vub|

b→s loop ~3 10-4 new physics, |Vts|

b→d loop ~ 10-6 new physics, |Vtd|

There are also b→s,dl+l- to complement the radiative modes

Not only BR are relevant: various asymmetries, spectra etc


What do they have in common?

INCLUSIVE EXCLUSIVE

OPE: non-pert physics described by B matrix elemnts of local operators can be extracted by exp suppressed by 1/mb

2

Form factors: in general computed by non pert methods (lattice, sum rules,...) symmetry can provide

normalization

Simplicity: ew or em currents probe the B dynamics

B

X

Simplicity is almost always destroyed in practical situations...


EXCLUSIVE

Determination of ADetermination of A

VCKM

A can be determined using |Vcb| or |Vts|

Two roads to |Vcb|

INCLUSIVE


|Vcb| from BD*l

At zero recoil, where rate vanishes.Despite extrapolation, exp error ~ 2%

Main problem is form factor F(1)

The non-pert quantities relevant for excl decays cannot be experimentally determined

Must be calculated but HQET helps.

Lattice QCD: F(1) = 0.91+0.03-0.04

Sum rules give consistent resultsNeeds unquenching (under way)Even slope may be calculable...

FB→D*(1) = ηA [1 - O(1/mb,1/mc)2]

BDl gives consistent but less precise results; lattice control is better

δVcb/Vcb~ 5% and agrees with inclusive det, despite contradictory exps

THE NON-PERT UNKNOWNSMUST BE CALCULATED,CANNOT BE MEASURED

B D*b c

d

l

v


The advantage of being The advantage of being inclusiveinclusive

ΛQCD«mb : inclusive decays admit systematic expansion in

ΛQCD/mb Non-pert corrections are generally small and can be controlled

Hadronization probability =1 because we sum over all statesApproximately insensitive to details of meson structure as ΛQCD«mb

(as long as one is far from perturbative singularities)

02

2

dqdqdE

d

l

can be expressed as double series in ααs s and and ΛQCD/mb

(OPE) with parton model as leading term No 1/mb

correction!


HQE = Heavy Quark Expansion

A double expansionA double expansion can be expressed in terms of structure

functions related to Im of0

2

2

dqdqdE

d

l

GbbcbDbcbbcJxJT 3

2

21)0()(OPE (HQE):

The leading term is parton model, ci are series in αs

New operators have non-vanishing expection values in B and are suppressed by powers of the energy released, Er~ mb-mc

No 1/mb correction! OPE predictions can be compared to exp only after SMEARING

and away from endpoints: they have no LOCAL meaning


Leptonic and hadronic spectra

Total rate gives CKM elmnts; global shape parameterstells us about B structure

OPE predictions can be compared to exp only after SMEARINGand away from endpoints: they have no LOCAL meaning


heavy quark massesmust be carefully defined:short distance, low scale

State of the artKnown corrections up to 1/mb

3: OPE/HQE predictions are only functions of possible cuts and of

1,2

O(1/mb2): mean

kin.energy of b in B

BbDibB

MB

|)(|2

1 22




1,2Gremm,Kapustin...1,2

33 , LSD

O(1/mb2): mean

kin.energy of b in B

BbDibB

MB

|)(|2

1 22


3

3

43

3

32

2

22

2

10

2

3

52

)()()()(1192 b

LS

b

D

b

G

bewcb

bFcl m

ram

ram

ram

rarzAVmG

Perturbative Corrections: full O(αs) and O(β0 αs2) available

For hadronic moments thanks to NEW calculations Trott Aquila,PG,Ridolfi,Uraltsev

Recent implementation for moments of lept and hadronic spectra including a cut on the lepton energy Bauer et al.,Uraltsev & PG



1,2Gremm,Kapustin...1,2

33 , LSD


Using moments to extract HQE parameters

432222 1.064.052.16.44.03.1 GeVmmMM DcbXX

Central moments can be VERY sensitive to HQE parameters

Experiments at Υ(4s) require a CUT on the lepton energy El>0.6-1.5 GeV.

Provided cut is not too severe (~1.3GeV)the cut moments give additional info

We do know something on HQE par.need to check consistency.

•MB*-MB fix G2= 0.35±0.03

•Sum rules: G2 2, ρD

3 -ρ3

LS...

BUT: OPE accuracy deteriorates for higher moments (getting sensitive to local effects)

Variance of mass distribution


Global fit to |Vcb|, BRsl, HQE parmts

Pioneer work by CLEO & Delphi employed less precise/completedata, some external constraints, and CLEO a different scheme

Not all points includedNo external constraint

LEPTONIC MOMENTS

Preliminary, O.Buchmuller


Global fit to |Vcb|, BRsl, HQE

parmts

HADRONICHADRONICMOMENTSMOMENTS

Preliminary, O.Buchmuller

Excellent agreement within exp and TH errors

Very similar results in a differentapproach/scheme, Bauer et al


H.Flaecher, CKM 2005


Bauer, Manohar, Ligeti, Luke, Trott 2005

Results in the 1S scheme

There are several differences:• perturbative quark mass scheme• expansion in inverse powers of mc

• handling of higher orders•estimate of th errors...


+unquenching+unquenching


Theoretical uncertainties are crucial for the fits

Missing higher power corrections

Intrinsic charm

Missing perturbative effects in the Wilson

coefficients: O(s2), O(αs/mb

2) etc

Duality violations

How can we estimate all this?Different recipes, results for |Vcb| unchanged


Testing parton-hadron Testing parton-hadron dualityduality

What is it?What is it? For all practical purposes: the OPE. No OPE, no duality

Do we expect violations?Do we expect violations? Yes, problems prevalently arise because OPE must be continued analytically. there are effects that cannot be described by the OPE, like hadronic thresholds. Expected small in semileptonic decays

Can we constrain them effectively?Can we constrain them effectively? in a self-consistent way: just check the OPE predictions. E.g. leptonic vs hadronic moments. Models may also give hints of how it

works

Caveats?Caveats? HQE depends on many parameters and we know only a few terms of the double expansion in αs and Λ/mb.


It is not just Vcb ...

HQE parameters describe universal properties of the B meson and of the quarks

• c and b masses can be determined with competitive accuracy (likely better than 70 and 50 MeV) mb-mc is already measured to better than 30 MeV: a benchmark for lattice QCD etc?

• It tests the foundations for inclusive measurements

• most Vub incl. determinations are sensitive to a shape function,

whose moments are related to μ2 etc,

• Bounds on , the slope of IW function (BD* form factor)

• ...

Need precision measurements to probe limits of HQE & testour th. framework


|V|Vubub| is the priority now| is the priority now

ρ = 0.210 ± 0.035 η = 0.339 ± 0.021

http://www.utfit.org


Strictly tree level


b→ulv exclusive

(CLEO only)

There is NO normalization of form f.s from HQ symmetry

New first unquenched resultslattice errors still ~15%

Sum rules good at low q2

lattice at high q2: complementeach other

Lattice (distant) goal is 5-6%

New strategy using combinationof rare B,D decays Grinstein& Pirjol


|Vub| (not so much) inclusive

|Vub| from total BR(bul) almost exactly like incl |Vcb| but we need kinematic cuts to avoid the ~100x larger bcl background:

mX < MD El > (MB2-MD

2)/2MB q2 > (MB-MD)2 ...

or combined (mX,q2) cuts

The cuts destroy convergenceof the OPE, supposed to workonly away from pert singularities

Rate becomes sensitive to “local”b-quark wave function properties (like Fermi motion at leading in 1/mb SHAPE function)


Luke, CKM workshop 2005


Each strategy has pros and cons

Luke, CKM workshop 2005


What do we know about f(k+)?

• Its moments can be expressed in terms of m.e. of local operators, those extracted from the b->c moments

• It can be extracted from b→s (see later)

• It can also be studied in b→ulv spectra (see

next)

• It gets renormalized and we have learned how (delicate interplay with pert contributions)


Vub incl. and exclusive

exclusiveexclusive

Intense theoretical activity:subleading shape functionsoptimization of cuts (P+,P- etc)weak annihilation contribs.Resum. pert. effectsrelation to bs spectrumSCET insight

A lot can be learned from exp

(on shape function from bs, WA, indirect constraints on s.f., subleading effects from cut dependence,...)

REQUIRES MANY COMPLEMENTARY MEASUREMENTS (affected by different uncert.)

There is no Best Method WE ARE ALREADY AT 10%New BRECO analyses; new results soon...


Cutting the cuts...New exp analyses basedon fully reconstructed events allow high discrimination of charmed final states

2004

Unfolded MX spectrum

Babar measured MX

moments. Results can beimproved by cutting in amilder way than usual

It’s time to start using b->u data to constrain sf!

Useful to validate theory

and constrain f(k+) & WA

PG,Ossola,Uraltsev


b → s transitions

Inclusive decays are described by OPE (except charm loop contributions!)

ΛQCD«mb«MW

mb«MW

Large L=log mb/MW must be resummed.

LO: αsnLn, NLO: αs

nLn-1

But many more operators appear

adding gluons

Tower of local opsOPE

bR sLLRb sFbmO

__

7

The current is not conserved and runs between MW and mb

We have AT LEAST 3 scales


The main ingredientsThe main ingredients

Process independent:Process independent:• The Wilson coefficients CThe Wilson coefficients Cii (encode the short

distance information, initial conditions)

• The Anomalous Dimension MatrixThe Anomalous Dimension Matrix (mixing among operators, determines the evolution of the coefficients,

allowing to resum large logs)

Process dependent:Process dependent: matrix elements

BB→ → XXssγγ : NLO QCD calculation completed, all results checked, EW , power corrections

BB→ → XXssll:ll: NNLO & EW calculation just completed,power corrections

cc


The charm mass problemmc enters the phase factor

due to normalization= 0.581±0.017

and the NLO matrix elements

As the related LO diagrams vanish, the definition of mc is aNNLO issue. Numerically very important because these are large NLO contributions: mc(mc)=1.25±0.10 GeV mc(mb)=0.85±0.11 GeV mc(pole)~1.5GeVBut pole mass has nothing to do with these loops

Changing mc/mb from 0.29 (pole) to 0.22 (MSbar) increases BRγ by 11%0.22 ±0.04 gives DOMINANT 6% theory errorgives DOMINANT 6% theory error

Misiak & PG


Error anatomy of BRError anatomy of BRγγ

Total error 8% dominated by charm mass Can be partially resolved by NNLO

Update under way

Misiak, PG 2001


Photon spectrum vs total BRThe OPE does not predict the

spectrum, only its global properties: the higher the cut the higher the uncertainty

Conversely, constraining the HQE parameters constrains the possible shape functions

Possible subleading shape functns effects in Vub applications

The shape function gets renormalized by perturbative effects: some complications may be better understood in SCET (Bauer & Manohar, Neubert et al)


Universality: spectrum of BXsγ

Motion of b quark inside B and gluon radiation smear the spike at mb/2

Belle: lower cut at 1.8GeV

The photon spectrum is very insen-sitive to new physics, can be used to study the B meson structure

<Eγ> = mb/2 + ... var<Eγ>

=μп2/12+...

Importance of extending to Eγmin

~ 1.8 GeV or

less for the determination of both the BR ANDthe HQE parameters Bigi Uraltsev

Info from radiative spectrum compatible with semileptonic moments

γs quarkb quark


results in two different schemes, agree well with b->clv


More cuts complications

μh

μi

μ0

μh~mb

μi~√Δmb

μ0~Δ=mb-2Ecut

The lower photon energy cut Ecut introduces two new scales

EVEN when local OPE works fine terms αs(Δ) could be large

non-pert domain

Neubert 2004


Neubert (II)• Need to disentangle 3 scales MultiScaleOPE

QCD SCET HQET local OPEμh μi μ0

How well can we predict the radiative tail?

•Neubert finds F(E >1.8GeV)=0.89±0.07, BR 3% lower, and theory error on BR 50% larger FUNDAMENTAL LIMITATION? • Main effect due to pert corrections whose scale is determined by higher orders (BLM etc): NNLO is the solution (at least to large extent)

• Sudakov resummation is irrelevant for Ecut <1.8

GeV

• New result of dominant 77 photon spectrum at O(αs

2)


The NNLO spectrum (dominant part)

Melnikov & Mitov 2005

BLM

NNLO

NLO

NNLO calculation very close to BLM

Non-BLM correctionschange BR by 0.5%

Situation seems under control

z=2E/mb

pole scheme


NNLO status report

• NNLO C7,8 matching completed Misiak, Steinhauser

• All 3loop NNLO ADM Gorbahn,Haisch,Misiak

• Parts of the 3loop NNLO matrix elements

Bieri et al & Asatrian et al

• 2loop matrix element of Q7 Czarnecki et al

• Dominant part of NNLO spectrum Melnikov Mitov

Still missing:• 4loop ADM• 3loop ME with charm• subdominant 2loop ME


b->slb->sl++ll- - : a more complicated : a more complicated case case

This decay mode is sensitive to different operators, hence to different new physics

Here large logs are generated even withoutQCD: LO αs

nLn+1, NLO αsnLn

,...

However, numerically the leading log issubdominant, yielding an awkward series:

in BR 1+ 0.7 (αs)+ 5.5 (αs2)+ ...


Error Anatomy for BRError Anatomy for BRllll

•Mtop dominant error 7%• scale uncertainty 5%•mb

pole = 4.80±0.15 GeV →5%• phase space factor 3%•No mc issue as charm enters at LO

TOTAL ERROR ~10%TOTAL ERROR ~10%

BUT: BUT: bottom uncertainty is not a fundamental limitation δmb

short distance ≈ 30-50 MeV

simply change scheme!

EXP: only inclusive rate,Belle (140fb-1): (4.4±0.8±0.8)x10-6

Babar(80fb-1): (5.6±1.5±1.3)x10-6

We get (4.6±0.8)x10-6 (mll>0.2GeV)

Bobeth,PG,Gorbahn,Haisch


the UT from excl radiative decaysthe UT from excl radiative decays

•Inclusive b->d experimentally impossible, but exclusive modes start being accessible

• Ratios of B→ρ / B→K* allow a determination of |Vtd/ Vts| that is independent of form factors in the limit of SU(3)

• Calculations rely on QCD factorization and on lattice/sum rules for the estimate of SU(3) violation (Beneke et al, Bosch Buchalla) power corrections apparently suppressed

•Neutral modes don’t have WA, ξ=1.2±0.1 (CKM 2005)

•LC sum rules errors large, Lattice calculations only exploratory…


An interesting deviation?

Impact on UT using only neutral modes:

BR(B0 →ρ0 )=0.6+1.9-1.4x10-7

Impact on UT using average of neutral and charged modes:

BR(B →ρ/ω )=(6.4± 2.7)x10-7


Summary of main theory limitations

processquantity

Th error

needs goal

B→D*lv |Vcb| ~4% New lattice results

1%

B→Xlv |Vcb|~1.5%

New pert calculations

<1%

B→π lv |Vub| ~15% Lattice developments

6%?

B→Xulv |Vub| ~10%More data synergy th/exp 5%

B→Xs BR ≲10% NNLO,MSOPE? <5%

B→ρ0/B→K*0

|Vtd|/ |Vts|

10-20%

Better understanding of th errors, lattice

?


No sign of No sign of deteriorationdeterioration

for higher cutsfor higher cuts

Kinetic scheme:Small pert correctionsMinimal set of parmts

No 1/mc expansion Uraltsev & PG

Paolo Gambino Beauty 2005 Assisi 1 Semileptonic and radiative B decays Paolo Gambino INFN Torino.

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Transcript of Paolo Gambino Beauty 2005 Assisi 1 Semileptonic and radiative B decays Paolo Gambino INFN Torino.